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AP EAMCET202316 May 2023Morning ShiftMathematicsProbabilityActual

A and B are independent events of a random experiment if and only if

Options

  1. AP ( A B ) P ( A B )
  2. BP ( A B )= P ( B A )
  3. CP ( A B ) P ( A B ^ C )
  4. DP(A B)=P (A B^C )

Correct answer

D. P(A B)=P (A B^C )

Step-by-step solution

Given that A and B are independent events. P(A B)=P(A) P(B)P(A B)= P(A B) P(B) = P(A) P(B) P(B) =P(A) ...(i) And P(B A)= P(B A) P(A) = P(B) P(A) P(A) =P(B) aligned & P (A B^C )= P (A B^C ) P (B^C ) = P(A)-P(A B) P (B^C ) & = P(A)-P(A) P(B) P (B^C ) = P(A)[1-P(B)] P (B^C ) aligned P (A B^C )= P(A) P (B^C ) P (B^C ) =P(A) ...(ii) From eqns. (i) and (ii) P(A B)=P (A B^C )

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